CN111242503A - Multi-target flexible job shop scheduling method based on two-layer genetic algorithm - Google Patents

Multi-target flexible job shop scheduling method based on two-layer genetic algorithm Download PDF

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CN111242503A
CN111242503A CN202010076205.3A CN202010076205A CN111242503A CN 111242503 A CN111242503 A CN 111242503A CN 202010076205 A CN202010076205 A CN 202010076205A CN 111242503 A CN111242503 A CN 111242503A
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张立果
黎向锋
唐浩
左敦稳
张丽萍
陆开胜
王建明
叶磊
王子旋
刘晋川
刘安旭
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Abstract

A multi-target flexible job shop scheduling method based on a double-layer genetic algorithm is characterized in that a traditional genetic algorithm is improved, so that the population optimized in a limited time by the genetic algorithm has higher quality; meanwhile, the solving mode of the traditional genetic algorithm to the multi-target problem is changed, a double-layer solving framework is provided, and compared with the traditional genetic algorithm, the solving quality is obviously improved. The invention optimizes the cross strategy and the mutation strategy and deletes the selection operator. The invention combines the improved genetic algorithm with a rapid non-dominated sorting and congestion degree calculation module, designs a special flow framework for the improved genetic algorithm, and calls the special flow framework as a double-layer genetic algorithm. The algorithm can obtain an excellent non-dominated solution set within a limited time, has good practicability and can be well applied to actual workshop scheduling.

Description

Multi-target flexible job shop scheduling method based on two-layer genetic algorithm
Technology neighborhood
The invention relates to a production scheduling technology, in particular to a flexible workshop height technology, and specifically relates to a multi-target flexible job workshop scheduling method based on a two-layer genetic algorithm.
Background
At present, the intense market competition is realized, and customers have explosive diversified and personalized requirements on products. The production mode of enterprise products gradually changes from being dominated by enterprises to being dominated by users. In the face of such changes, the traditional manual scheduling method can no longer meet the requirements of enterprises, and the problem must be handled by an informatization and intelligentized means. The workshop scheduling technology is one of the key factors for realizing high efficiency, high flexibility and high reliability of manufacturing enterprises. When a workshop scheduling problem is generally researched, the workshop scheduling problem is researched on the basis of a classic job workshop scheduling problem: each workpiece comprises a plurality of working procedures, each working procedure can be processed on one machine only and can be processed once, the processing time is determined, and the sequence of the working procedures of each workpiece is restricted. The flexible job shop scheduling problem is studied on the basis that each process can be processed on a given plurality of machines, compared with the job shop scheduling.
In reality, for the flexible job shop scheduling problem, a manager often has a requirement for multiple optimization targets. However, the solution obtained by only solving for a single target often appears very poor on other targets, and does not meet the requirement of actual processing, so that the solution of the multi-target scheduling problem is very necessary. The genetic algorithm aiming at the multi-objective optimization problem generally screens the population of the genetic algorithm by using a rapid non-dominated sorting and congestion degree calculation method, but non-dominated solution sets obtained by the genetic algorithm are usually concentrated in a certain specific range, excellent solutions cannot be obtained under the global condition, the genetic algorithm often falls into the local optimal predicament after iteration for multiple times, and at the moment, the population diversity is not excellent enough, and the search cannot be continued.
In summary, in order to improve the production efficiency of a workshop and reduce the operation cost of the workshop, it is necessary to find an efficient artificial intelligence algorithm to optimize the scheduling problem of the multi-target flexible job workshop.
Disclosure of Invention
The invention aims to solve the problems that when a single genetic algorithm used by the conventional workshop scheduling is applied to multi-target search, the obtained non-dominated solution sets are always concentrated in a certain specific range, excellent solutions cannot be obtained under the global condition, the method often falls into the local optimal dilemma after iteration for multiple times, and at the moment, the searching cannot be continued due to the insufficient excellent population diversity.
The technical scheme of the invention is as follows:
a multi-target flexible job shop scheduling method based on a double-layer genetic algorithm is characterized in that a traditional genetic algorithm is improved, so that the population optimized in a limited time by the genetic algorithm has higher quality; meanwhile, the solving mode of the traditional genetic algorithm to the multi-target problem is changed, a double-layer solving framework is provided, compared with the traditional genetic algorithm, the solving quality is obviously improved, and the method comprises the following steps:
firstly, an encoding mode with a machine sequence and a process sequence matched is adopted as an encoding format: each gene in the machine sequence represents the processing machine selected by the process of the work piece; in the process sequence, each gene represents a workpiece number, and represents the next process according to the position of the workpiece number appearing in a chromosome;
secondly, a decoding mode of full active scheduling is adopted as a decoding mode: the method has the following two specific modes, namely greedy decoding and reversed chromosome decoding;
wherein:
greedy decoding: according to the sequence of the process sequence of the chromosome, inserting the process into the corresponding best feasible machining of the machine under the condition of meeting the process sequence constraint;
and (3) overturning chromosome decoding: according to the chromosome process sequence, the processes are sorted from back to front, namely, the processes with larger work sequence numbers are firstly sorted and then the processes with smaller work sequence numbers are sorted on the premise of meeting the process constraint, and meanwhile, the process blocks are sorted forwards as much as possible according to the greedy decoding rule. The real processing process is to turn over the decoded Gantt chart for guiding the real processing process;
the decoding mode of the full active scheduling is to select a decoding mode with a smaller objective function value from the two decoding modes as an actually used decoding mode;
thirdly, initialization:
if the objective function is that the maximum completion time is minimum, the following initialization mode is adopted: the initialization method aiming at the machine sequence adopts the schemes of global search, local search and random initialization, the proportions of the schemes are respectively set to be 0.2, 0.2 and 0.6, and simultaneously, the schemes of the longest residual processing time, the largest residual operand and the random selection are adopted aiming at the sequence of the machine sequence, wherein the ratios of the schemes are respectively as follows: 0.4, 0.2; if the target function is other, adopting a completely random initialization method;
fourth, the cross mode:
the crossing mode adopted by the process sequence crossing selects a priority operation crossing operator and a global position crossing operator, and the two crossing operators are used with a probability of 50 percent respectively;
the machine sequence crossing mode adopts a random crossing mode, namely an auxiliary sequence with the length of the machine sequence and the value of 0 or 1 is randomly generated, when the element in the sequence is zero, the machine sequence generated after crossing selects the gene of the parent 1 at the corresponding position, otherwise, the gene of the parent 2 is selected;
fifth, variation:
randomly selecting a gene from the machine sequence of the chromosome aiming at the variation of the machine sequence of the chromosome, finding out the process to which the gene belongs according to the gene, and randomly selecting a machine number from the selectable machine set to replace the gene; randomly selecting a gene from the process sequence according to the variation of the process sequence of the chromosome, and randomly selecting a position from the process sequence to perform insertion operation;
sixth, improve crossover and mutation strategies:
according to the crossing mode, crossing the process sequence for N times, wherein N is the number of machines; the machine sequence is crossed for M times every time the process sequence is crossed, wherein M is the number of the workpieces; after crossing, symbiotic forming 2 XNXM chromosomes, dividing the chromosomes into two groups, then respectively adding two father chromosomes into the two groups, and taking out two optimal chromosomes as the next generation chromosomes;
according to the mutation mode, after carrying out mutation operation on chromosomes meeting the mutation probability in the current population, putting the mutated chromosomes into a set, comparing the mutated chromosomes with the worst chromosomes in the current population, and replacing if the mutated chromosomes are better than the worst chromosomes in the current population, or not changing;
seventh, delete selection operator: by deleting the selection operator, the stability and the search depth of the algorithm can be effectively improved;
eighth, the improved genetic algorithm module:
step 1, setting parameters of population scale N, crossing rate α and variation rate β;
step 2: if no initial population exists, generating an initial population by using a certain initialization strategy according to the current objective function, otherwise, using the transferred initial population. The number of evolutions was set to 0.
And step 3: an objective function value is calculated for each chromosome, which value characterizes the degree of goodness of the individual.
And 4, crossing, namely, disordering the population, dividing every two chromosomes into a group from front to back, randomly generating a probability value for each group of chromosomes to judge whether the probability value is less than the crossing probability α, and if the probability value is less than the crossing probability α, carrying out crossing operation on the chromosomes according to a crossing strategy.
And 5, carrying out mutation, randomly generating a probability value for each element in the population, judging whether the probability value is smaller than the mutation probability β, and if the probability value is smaller than the mutation probability β, optimizing the population according to a mutation strategy.
Step 6: and (4) self-increasing the evolution times, if the evolution times exceed the maximum iteration times, entering the step 7, and otherwise, returning to the step 3.
And 7: and outputting the current chromosome population.
Only the genetic algorithm module is improved to be insufficient to meet the requirement of multi-objective solution, and a certain algorithm framework is required to be used for well playing the function of the module;
ninth, the fast non-dominated sorting and congestion degree calculation module is used for preferentially outputting the elements with larger congestion degree values:
because the multi-objective optimization problem is processed, a method must be used for sequencing the elements in the population; assuming that A and B are one solution of the multi-objective optimization problem; if the value of A under each target function is not inferior to that of B under each target function, and at least one function value of A is superior to that of B, A is used for dominating B. If A does not dominate B and B does not dominate A, it is said that A is not different from B; according to the domination relationship among elements in the population, the population can be divided into multiple layers according to the priority; for elements in the same layer, the crowdedness relation exists among the elements; the output rule of the module is to output the elements belonging to the superior hierarchy preferentially, and output the elements with larger congestion value preferentially when the hierarchies are the same;
tenth, optimizing the scheduling scheme by using a double-layer genetic algorithm framework:
the algorithm comprises the following steps of: wherein steps 1 to 4 belong to a first layer and steps 5 to 10 belong to a second layer;
step 1: each target generates a chromosome population of size N; when the objective function is the minimum maximum completion time, using an exclusive initialization mode of the objective function, otherwise, using a random initialization mode;
step 2: respectively putting each population into a genetic algorithm module with different set objective functions, setting the maximum iteration times of the population as S1, and outputting the optimized population;
and step 3: mixing the optimized populations of each target together, and respectively calculating the maximum value f of each target function in the current populationjmaxAnd minimum value fjminAnd recording;
and 4, step 4: selecting the optimal N chromosomes as the initial chromosome population of the next layer by using rapid non-dominated sorting and crowding calculation;
and 5: if the first optimization in the second layer is carried out, the initial population transmitted from the first layer is used and stored as the non-dominated solution of the current population, meanwhile, the number of optimization times is set to be 1, otherwise, the population obtained by the second layer optimization is added with the population transmitted from the first layer, and the optimal N chromosomes are selected as the initial population by using a rapid non-dominated sorting and congestion degree calculation strategy;
step 6: generating an objective function according to the following formula, wherein each objective function has an associated weight λjFor random generation, the sum of the weights is 1, and the objective function is taken as the objective function of the improved genetic algorithm module;
an objective function:
Figure BDA0002378555580000041
wherein: f. ofiAn objective function value representing the ith chromosome; k is the target number; f. ofijRepresenting an objective function value corresponding to a jth target of the ith chromosome; f. ofjmax、fjminA maximum value and a minimum value representing respective objective functions obtained in the first layer; lambda [ alpha ]jRepresents the weight occupied by each target;
and 7: putting the population obtained in the step 5 into an improved genetic algorithm module as an initial population of the module, wherein the target function is the target function generated in the step 6, and the maximum iteration number of the genetic algorithm module is set to be S2;
and 8: and (4) performing rapid non-dominant sorting and congestion degree calculation on the population obtained in the step (7), and reserving a non-dominant solution. The optimization times are increased by 1;
and step 9: judging whether the optimizing times reach the maximum optimizing times R, if so, entering the step 10, otherwise, returning to the step 5;
step 10: and (4) mixing the non-dominated solution sets reserved in the step (8), carrying out rapid non-dominated sorting and outputting a non-dominated solution.
The invention has the beneficial effects that:
the method solves the problems that the stability of a related algorithm in the multi-target flexible job shop scheduling is poor, the search depth is not enough, and the deep search of a single target in multiple targets cannot be carried out.
The invention optimizes the cross strategy and the mutation strategy and deletes the selection operator through the improved genetic algorithm. Based on the improved genetic algorithm, the invention combines the improved genetic algorithm with a rapid non-dominated sorting and congestion degree calculation module and designs a special flow framework (double-layer genetic algorithm) for the improved genetic algorithm. The algorithm can obtain an excellent non-dominated solution set within a limited time, has good practicability and can be well applied to actual workshop scheduling.
Drawings
FIG. 1 is a block diagram of a two-tier genetic algorithm flow scheme of the present invention.
FIG. 2 is a block diagram of an improved genetic algorithm used in the present invention.
FIG. 3 is a Gantt chart with the non-dominated solution objective function values [40, 38, 162] found for case Mk 01.
Detailed Description
The invention will be further described with reference to the following examples of the drawings.
As shown in fig. 1-2.
A multi-target flexible job shop scheduling method based on a double-layer genetic algorithm improves the traditional genetic algorithm, so that the population optimized in a limited time by the genetic algorithm has higher quality; meanwhile, the solving mode of the traditional genetic algorithm to the multi-target problem is changed, a double-layer solving framework is provided, compared with the traditional genetic algorithm, the solving quality is obviously improved, and the method comprises the following steps:
firstly, an encoding mode with a machine sequence and a process sequence matched is adopted as an encoding format: each gene in the machine sequence represents the processing machine selected by the process of the work piece; in the process sequence, each gene represents a workpiece number, and represents the next process according to the position of the workpiece number appearing in a chromosome;
secondly, a decoding mode of full active scheduling is adopted as a decoding mode: the method has the following two specific modes, namely greedy decoding and reversed chromosome decoding;
wherein:
greedy decoding: according to the sequence of the process sequence of the chromosome, inserting the process into the corresponding best feasible machining of the machine under the condition of meeting the process sequence constraint;
and (3) overturning chromosome decoding: according to the chromosome process sequence, the processes are sorted from back to front, namely, the processes with larger work sequence numbers are firstly sorted and then the processes with smaller work sequence numbers are sorted on the premise of meeting the process constraint, and meanwhile, the process blocks are sorted forwards as much as possible according to the greedy decoding rule. The real processing process is to turn over the decoded Gantt chart for guiding the real processing process;
the decoding mode of the full active scheduling is to select a decoding mode with a smaller objective function value from the two decoding modes as an actually used decoding mode;
thirdly, initialization:
if the objective function is that the maximum completion time is minimum, the following initialization mode is adopted: the initialization method aiming at the machine sequence adopts the schemes of global search, local search and random initialization, the proportions of the schemes are respectively set to be 0.2, 0.2 and 0.6, and simultaneously, the schemes of the longest residual processing time, the largest residual operand and the random selection are adopted aiming at the sequence of the machine sequence, wherein the ratios of the schemes are respectively as follows: 0.4, 0.2; if the target function is other, adopting a completely random initialization method;
fourth, the cross mode:
the crossing mode adopted by the process sequence crossing selects a priority operation crossing operator and a global position crossing operator, and the two crossing operators are used with a probability of 50 percent respectively;
the machine sequence crossing mode adopts a random crossing mode, namely an auxiliary sequence with the length of the machine sequence and the value of 0 or 1 is randomly generated, when the element in the sequence is zero, the machine sequence generated after crossing selects the gene of the parent 1 at the corresponding position, otherwise, the gene of the parent 2 is selected;
fifth, variation:
randomly selecting a gene from the machine sequence of the chromosome aiming at the variation of the machine sequence of the chromosome, finding out the process to which the gene belongs according to the gene, and randomly selecting a machine number from the selectable machine set to replace the gene; randomly selecting a gene from the process sequence according to the variation of the process sequence of the chromosome, and randomly selecting a position from the process sequence to perform insertion operation;
sixth, improve crossover and mutation strategies:
according to the crossing mode, crossing the process sequence for N times, wherein N is the number of machines; the machine sequence is crossed for M times every time the process sequence is crossed, wherein M is the number of the workpieces; after crossing, symbiotic forming 2 XNXM chromosomes, dividing the chromosomes into two groups, then respectively adding two father chromosomes into the two groups, and taking out two optimal chromosomes as the next generation chromosomes;
according to the mutation mode, after carrying out mutation operation on chromosomes meeting the mutation probability in the current population, putting the mutated chromosomes into a set, comparing the mutated chromosomes with the worst chromosomes in the current population, and replacing if the mutated chromosomes are better than the worst chromosomes in the current population, or not changing;
seventh, delete selection operator: by deleting the selection operator, the stability and the search depth of the algorithm can be effectively improved;
eighth, the improved genetic algorithm module: as shown in fig. 2.
Step 1, setting parameters of population scale N, crossing rate α and variation rate β;
step 2: if no initial population exists, generating an initial population by using a certain initialization strategy according to the current objective function, otherwise, using the transferred initial population. The number of evolutions was set to 0.
And step 3: an objective function value is calculated for each chromosome, which value characterizes the degree of goodness of the individual.
And 4, crossing, namely, disordering the population, dividing every two chromosomes into a group from front to back, randomly generating a probability value for each group of chromosomes to judge whether the probability value is less than the crossing probability α, and if the probability value is less than the crossing probability α, carrying out crossing operation on the chromosomes according to a crossing strategy.
And 5, carrying out mutation, randomly generating a probability value for each element in the population, judging whether the probability value is smaller than the mutation probability β, and if the probability value is smaller than the mutation probability β, optimizing the population according to a mutation strategy.
Step 6: and (4) self-increasing the evolution times, if the evolution times exceed the maximum iteration times, entering the step 7, and otherwise, returning to the step 3.
And 7: and outputting the current chromosome population.
Only the genetic algorithm module is improved to be insufficient to meet the requirement of multi-objective solution, and a certain algorithm framework is required to be used for well playing the function of the module;
ninth, the fast non-dominated sorting and congestion degree calculation module is used for preferentially outputting the elements with larger congestion degree values:
because the multi-objective optimization problem is processed, a method must be used for sequencing the elements in the population; assuming that A and B are one solution of the multi-objective optimization problem; if the value of A under each target function is not inferior to that of B under each target function, and at least one function value of A is superior to that of B, A is used for dominating B. If A does not dominate B and B does not dominate A, it is said that A is not different from B; according to the domination relationship among elements in the population, the population can be divided into multiple layers according to the priority; for elements in the same layer, the crowdedness relation exists among the elements; the output rule of the module is to output the elements belonging to the superior hierarchy preferentially, and output the elements with larger congestion value preferentially when the hierarchies are the same;
tenth, optimizing the scheduling scheme by using a double-layer genetic algorithm framework:
the algorithm comprises the following steps of: wherein steps 1 to 4 belong to a first layer and steps 5 to 10 belong to a second layer; as shown in fig. 1.
Step 1: each target generates a chromosome population of size N; when the objective function is the minimum maximum completion time, using an exclusive initialization mode of the objective function, otherwise, using a random initialization mode;
step 2: respectively putting each population into a genetic algorithm module with different set objective functions, setting the maximum iteration times of the population as S1, and outputting the optimized population;
and step 3: mixing the optimized populations of each target together, and respectively calculating the maximum value f of each target function in the current populationjmaxAnd minimum value fjminAnd recording;
and 4, step 4: selecting the optimal N chromosomes as the initial chromosome population of the next layer by using rapid non-dominated sorting and crowding calculation;
and 5: if the first optimization in the second layer is carried out, the initial population transmitted from the first layer is used and stored as the non-dominated solution of the current population, meanwhile, the number of optimization times is set to be 1, otherwise, the population obtained by the second layer optimization is added with the population transmitted from the first layer, and the optimal N chromosomes are selected as the initial population by using a rapid non-dominated sorting and congestion degree calculation strategy;
step 6: generating an objective function according to the following formula, wherein eachThe correlation weight λ of the objective functionjFor random generation, the sum of the weights is 1, and the objective function is taken as the objective function of the improved genetic algorithm module;
an objective function:
Figure BDA0002378555580000081
wherein: f. ofiAn objective function value representing the ith chromosome; k is the target number; f. ofijRepresenting an objective function value corresponding to a jth target of the ith chromosome; f. ofjmax、fjminA maximum value and a minimum value representing respective objective functions obtained in the first layer; lambda [ alpha ]jRepresents the weight occupied by each target;
and 7: putting the population obtained in the step 5 into an improved genetic algorithm module as an initial population of the module, wherein the target function is the target function generated in the step 6, and the maximum iteration number of the genetic algorithm module is set to be S2;
and 8: and (4) performing rapid non-dominant sorting and congestion degree calculation on the population obtained in the step (7), and reserving a non-dominant solution. The optimization times are increased by 1;
and step 9: judging whether the optimizing times reach the maximum optimizing times R, if so, entering the step 10, otherwise, returning to the step 5;
step 10: and (4) mixing the non-dominated solution sets reserved in the step (8), carrying out rapid non-dominated sorting and outputting a non-dominated solution.
Example (b):
as shown in fig. 3.
Take the Mk01 case as an example, the case is a classic flexible job shop scheduling case with 10 workpieces, 6 optional processing procedures and a total procedure number of 55, and the maximum workpiece completion time f is taken as the scheduling case1Maximum machine load f2, total machine load f3And performing flexible job shop scheduling multi-objective optimization for the optimization objective.
The detailed data of the Mk01 case are shown in table 1:
Figure BDA0002378555580000091
Figure BDA0002378555580000101
the non-dominant fronts that can be found using this case are shown in table 2:
Figure BDA0002378555580000102
the present invention is not concerned with parts which are the same as or can be implemented using prior art techniques.

Claims (5)

1. A multi-target flexible job shop scheduling method based on a double-layer genetic algorithm is characterized in that a traditional genetic algorithm is improved, so that the population optimized in a limited time by the genetic algorithm has higher quality; meanwhile, the solving mode of the traditional genetic algorithm to the multi-target problem is changed, a double-layer solving framework is provided, compared with the traditional genetic algorithm, the solving quality is obviously improved, and the method comprises the following steps:
firstly, an encoding mode with a machine sequence and a process sequence matched is adopted as an encoding format: each gene in the machine sequence represents the processing machine selected by the process of the work piece; in the process sequence, each gene represents a workpiece number, and represents the next process according to the position of the workpiece number appearing in a chromosome;
secondly, a decoding mode of full active scheduling is adopted as a decoding mode: the method has the following two specific modes, namely greedy decoding and reversed chromosome decoding;
wherein:
greedy decoding: according to the sequence of the process sequence of the chromosome, inserting the process into the corresponding best feasible machining of the machine under the condition of meeting the process sequence constraint;
and (3) overturning chromosome decoding: according to the chromosome process sequence, the processes are sorted from back to front, namely, the processes with larger work sequence numbers are firstly sorted and then the processes with smaller work sequence numbers are sorted on the premise of meeting the process constraint, and meanwhile, the process blocks are sorted forwards as much as possible according to the greedy decoding rule. The real processing process is to turn over the decoded Gantt chart for guiding the real processing process;
the decoding mode of the full active scheduling is to select a decoding mode with a smaller objective function value from the two decoding modes as an actually used decoding mode;
thirdly, initialization:
if the objective function is that the maximum completion time is minimum, the following initialization mode is adopted: the initialization method aiming at the machine sequence adopts the schemes of global search, local search and random initialization, and simultaneously adopts the scheme of selecting the longest residual processing time, the most residual operands and the random selection according to the priority for the sequencing of the machine sequence; if the target function is other, adopting a completely random initialization method;
fourth, the cross mode:
the crossing mode adopted by the process sequence crossing selects a priority operation crossing operator and a global position crossing operator, and the two crossing operators are used with a probability of 50 percent respectively;
the machine sequence crossing mode adopts a random crossing mode, namely an auxiliary sequence with the length of the machine sequence and the value of 0 or 1 is randomly generated, when the element in the sequence is zero, the machine sequence generated after crossing selects the gene of the parent 1 at the corresponding position, otherwise, the gene of the parent 2 is selected;
fifth, variation:
randomly selecting a gene from the machine sequence of the chromosome aiming at the variation of the machine sequence of the chromosome, finding out the process to which the gene belongs according to the gene, and randomly selecting a machine number from the selectable machine set to replace the gene; randomly selecting a gene from the process sequence according to the variation of the process sequence of the chromosome, and randomly selecting a position from the process sequence to perform insertion operation;
sixth, improve crossover and mutation strategies:
according to the crossing mode, crossing the process sequence for N times, wherein N is the number of machines; the machine sequence is crossed for M times every time the process sequence is crossed, wherein M is the number of the workpieces; after crossing, symbiotic forming 2 XNXM chromosomes, dividing the chromosomes into two groups, then respectively adding two father chromosomes into the two groups, and taking out two optimal chromosomes as the next generation chromosomes;
according to the mutation mode, after carrying out mutation operation on chromosomes meeting the mutation probability in the current population, putting the mutated chromosomes into a set, comparing the mutated chromosomes with the worst chromosomes in the current population, and replacing if the mutated chromosomes are better than the worst chromosomes in the current population, or not changing;
seventh, delete selection operator: by deleting the selection operator, the stability and the search depth of the algorithm can be effectively improved;
eighth, a genetic algorithm module is improved.
Only the genetic algorithm module is improved to be insufficient to meet the requirement of multi-objective solution, and a certain algorithm framework is required to be used for well playing the function of the module;
ninth, the fast non-dominated sorting and congestion degree calculation module is used for preferentially outputting the elements with larger congestion degree values:
because the multi-objective optimization problem is processed, a method must be used for sequencing the elements in the population; assuming that A and B are one solution of the multi-objective optimization problem; if the value of A under each target function is not inferior to that of B under each target function, and at least one function value of A is superior to that of B, A is used for dominating B. If A does not dominate B and B does not dominate A, it is said that A is not different from B; according to the domination relationship among elements in the population, the population can be divided into multiple layers according to the priority; for elements in the same layer, the crowdedness relation exists among the elements; the output rule of the module is to output the elements belonging to the superior hierarchy preferentially, and output the elements with larger congestion value preferentially when the hierarchies are the same;
tenth, optimizing the scheduling scheme by using a double-layer genetic algorithm framework:
the algorithm comprises the following steps of: wherein steps 1 to 4 belong to a first layer and steps 5 to 10 belong to a second layer;
step 1: each target generates a chromosome population of size N; when the objective function is the minimum maximum completion time, using an exclusive initialization mode of the objective function, otherwise, using a random initialization mode;
step 2: respectively putting each population into a genetic algorithm module with different set objective functions, setting the maximum iteration times of the population as S1, and outputting the optimized population;
and step 3: mixing the optimized populations of each target together, and respectively calculating the maximum value f of each target function in the current populationjmaxAnd minimum value fjminAnd recording;
and 4, step 4: selecting the optimal N chromosomes as the initial chromosome population of the next layer by using rapid non-dominated sorting and crowding calculation;
and 5: if the first optimization in the second layer is carried out, the initial population transmitted from the first layer is used and stored as the non-dominated solution of the current population, meanwhile, the number of optimization times is set to be 1, otherwise, the population obtained by the second layer optimization is added with the population transmitted from the first layer, and the optimal N chromosomes are selected as the initial population by using a rapid non-dominated sorting and congestion degree calculation strategy;
step 6: generating an objective function according to the following formula, wherein each objective function has an associated weight λjFor random generation, the sum of the weights is 1, and the objective function is taken as the objective function of the improved genetic algorithm module;
an objective function:
Figure FDA0002378555570000031
wherein: f. ofiAn objective function value representing the ith chromosome; k is the target number; f. ofijRepresenting an objective function value corresponding to a jth target of the ith chromosome; f. ofjmax、fjminA maximum value and a minimum value representing respective objective functions obtained in the first layer; lambda [ alpha ]jRepresents the weight occupied by each target;
and 7: putting the population obtained in the step 5 into an improved genetic algorithm module as an initial population of the module, wherein the target function is the target function generated in the step 6, and the maximum iteration number of the genetic algorithm module is set to be S2;
and 8: and (4) performing rapid non-dominant sorting and congestion degree calculation on the population obtained in the step (7), and reserving a non-dominant solution. The optimization times are increased by 1;
and step 9: judging whether the optimizing times reach the maximum optimizing times R, if so, entering the step 10, otherwise, returning to the step 5;
step 10: and (4) mixing the non-dominated solution sets reserved in the step (8), carrying out rapid non-dominated sorting and outputting a non-dominated solution.
2. The method of claim 1, wherein said improved genetic algorithm comprises the steps of:
step 1, setting parameters of population scale N, crossing rate α and variation rate β;
step 2: if no initial population exists, generating an initial population by using a certain initialization strategy according to the current objective function, otherwise, using the transferred initial population. Setting the evolution times to be 0;
and step 3: calculating an objective function value of each chromosome, wherein the value represents the quality degree of the individual;
step 4, crossing, namely, disordering the population, dividing every two chromosomes into a group from front to back, randomly generating a probability value for each group of chromosomes to judge whether the probability value is less than the crossing probability α, and if the probability value is less than the crossing probability α, carrying out crossing operation on the chromosomes according to a certain crossing strategy;
step 5, mutation, namely randomly generating a probability value for each element in the population to judge whether the probability value is less than β, and if the probability value is less than β, performing mutation operation on the elements according to a certain mutation strategy;
step 6: the evolution times are increased automatically, if the evolution times exceed the maximum iteration times, the step 7 is carried out, otherwise, the step 3 is carried out;
and 7: and outputting the current chromosome population.
3. The method of claim 2, wherein said improved interleaving strategy comprises the steps of:
step 1: the process sequence is crossed for N times, wherein N is the number of machines; the machine sequence is crossed for M times every time the process sequence is crossed, wherein M is the number of the workpieces;
step 2: after crossing, symbiotic to 2 XNXM chromosomes, then adding two father chromosomes into the chromosome set generated by crossing, and taking out two optimal chromosomes as next generation chromosomes.
4. The method of claim 2, wherein the improved mutation strategy comprises the steps of:
step 1: a gene is randomly selected from the machine sequences of the chromosome according to the variation of the machine sequences of the chromosome, and a machine number is randomly selected from the selectable machine set according to the process to which the gene belongs to replace the gene. Randomly selecting a gene from the process sequence according to the variation of the process sequence of the chromosome, and randomly selecting a position from the process sequence to perform insertion operation;
step 2: after mutation operation is carried out on chromosomes meeting the mutation probability in the current population, the chromosomes after mutation are put into a set and compared with the worst chromosome in the current population, if the chromosome is better than the worst chromosome, the chromosome is replaced, otherwise, the chromosome is not changed.
5. Initialization method according to claim 1, characterized in that when the optimization objective is maximum workpiece completion time, the machine sequence uses a method comprising: the initialization method comprises the following steps of global selection, local selection and random selection, wherein the ratio of the three methods in an initialization population is as follows: 0.2, 0.6; the process sequence comprises the following steps: the method comprises the following steps of (1) initializing with the longest residual processing time, the largest residual operand and random selection, wherein the ratios of the three methods in an initialization population are as follows: 0.4, 0.2.
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